Aibing Zhang

Effect of cracking on the thermoelectric conversion efficiency of thermoelectric materials

Analytical solutions for a rectangular thermoelectric plate with a crack under combined electrical and temperature loadings are obtained. The electric current density and energy flux intensity factors at the crack tip are calculated. The effective thermoelectric properties are obtained. From the results, it is found that both effective electric and heat conductivities are reduced by increasing the crack size. However, the thermoelectric conversion efficiency of the thermoelectric plate is independent of the crack size if the crack face boundary conditions are assumed to be electrically and thermally insulated. In addition, the effect of thermoelectric properties and size of an inclusion on the thermoelectric conversion efficiency is also discussed, and the condition for high efficiency thermoelectric materials is identified. This is the first theoretical paper to study the effect of cracking on the thermoelectric properties by a rigorous inference of mathematics and physics.

Contact Zone Approach for an Electrically Impermeable Crack in Piezoelectric Materials Under Thermal-Mechanical Loading

A partial contact zone model is developed for the stress and electric displacement fields due to the obstruction of a uniform heat flux by an electrically impermeable crack in piezoelectric materials. Greens function method is used to reduce the problem to a set of singular integral equations that are solved in closed form. When the crack is assumed to be traction free, the crack opening displacement is found to be negative over one-half of the crack unless a sufficiently large far field tensile stress is superposed. The problem is reformulated assuming a contact zone at one crack tip. The extent of this zone, the stress and electric displacement intensity factors at each crack tip are obtained as functions of the applied mechanical stress and heat flux.

On the coupling effects of piezoelectricity and flexoelectricity in piezoelectric nanostructures

Flexoelectricity is a novel kind of electromechanical coupling phenomenon that is prevalent in all solid dielectrics and usually of vital importance in nanostructures and soft materials. Although the fundamental theory of flexoelectric solids and related beam or plate theories were extensively studied in recent years, the coupling effect of flexoelectricity and piezoelectricity in piezoelectric nanostructures has not been completely clarified yet. In the present work, a geometrically nonlinear piezoelectric plate model is established with a focus on the coupling effect. The constitutive equations for piezoelectric plates are derived under both the electrically short-circuit and open-circuit conditions. It is found that due to the coupling between flexoelectricity and piezoelectricity, stretching-bending coupling stiffness arises in the homogeneous plate and its specific value relies on the applied electrical boundary conditions. The effects of the flexoelectric-piezoelectric coupling on the effective mech...

An analysis of thickness-shear vibrations of circular quartz crystal plates

Quartz crystal resonators of circular type are widely used for frequency control and detection functions with the quartz crystal plate vibrating at the thickness-shear mode. Naturally, vibrations of circular quartz crystal plates are of great interests in the design and optimization of resonators. We have derived the Mindlin plate equations for the thickness-shear vibrations of circular plates in a systematic manner. We have further proved that the thickness-shear vibrations of circular plates are consistent with rectangular plates in dispersion relations. By truncating the infinite two-dimensional equations for the thickness-shear vibrations, we obtained a set of equations with only selected vibration modes. Solving the coupled equations for thickness-shear vibration frequencies and mode shapes, we can use these results for the optimal selection of plate parameters to improve performance of resonators. The analytical equations and solution procedure are important in the analysis of quartz crystal vibrations.